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The excitation function for quasielastic scattering of the weakly bound projectile $^{6}\mathrm{Li}$ on a $^{159}\mathrm{Tb}$ target, at large backward angle, has been measured at energies around the Coulomb barrier. The corresponding quasielastic barrier distribution has been extracted from the experimental cross sections, both including and excluding the $\ensuremath{\alpha}$ particles produced in the reaction. The quasielastic scattering cross sections, excluding the $\ensuremath{\alpha}$ particles, have been analyzed in the framework of coupled channels calculations. The centroid of the quasielastic barrier distribution, including the $\ensuremath{\alpha}$ particles, is found to shift towards higher energy relative to the centroid of the fusion barrier distribution for the system. This has been attributed to the low $\ensuremath{\alpha}$-breakup threshold of the nucleus $^{6}\mathrm{Li}$.

We study the quasifission and fusion-fission lifetimes for a number of fusion reactions used to synthesize the superheavy element $Z=120$ using a statistical method within the framework of the dinuclear system model. In particular, influence of the target orientation and angular momentum on such lifetimes have been investigated. The quasifission and fusion-fission lifetimes have been compared very well with that of available experiments on successful superheavy element synthesis. We notice further the predicted quasifission and fusion-fission lifetimes of the projectile-target combinations used for the synthesis of the superheavy element $Z=120$ also show the similar trend. Furthermore, the fusion-fission lifetime is seen to somewhat decrease with the increase of the angular momentum as well as beam energy. Little effect is seen on fusion barrier of the reaction and fission barrier of superheavy compound nucleus. Variation of quasifission lifetime is also not much with orientation angle, beam energy and fission barrier of the superheavy compound nuclei. Hence, this lifetime study does not provide any good reason why the attempted reactions have failed to synthesize the superheavy nuclei $Z=120$. Furthermore, consideration of the fusion barrier, fissility, mass asymmetry, deformation parameter, fission barrier, etc., leads us to reveal that optimal colliding energy is important to have the largest evaporation residue cross section for any chosen reaction so that it is well within the measurable limit for a specific experimental set up.

Quasielastic scattering excitation function at large backward angle has been measured for the weakly bound system $^{7}\mathrm{Li}+^{159}\mathrm{Tb}$ at energies around the Coulomb barrier. The corresponding quasielastic barrier distribution has been derived from the excitation function, both including and excluding the $\ensuremath{\alpha}$ particles produced in the reaction. The centroid of the barrier distribution obtained after inclusion of $\ensuremath{\alpha}$ particles was found to be shifted higher in energy, compared with the distribution excluding the $\ensuremath{\alpha}$ particles. The quasielastic data, excluding the $\ensuremath{\alpha}$ particles, have been analyzed in the framework of continuum discretized coupled-channels calculations. The quasielastic barrier distribution for $^{7}\mathrm{Li}+^{159}\mathrm{Tb}$, has also been compared with the fusion barrier distribution for the system.

We develop a novel approach to fusion reactions for syntheses of superheavy elements, which combines the time-dependent Hartree-Fock (TDHF) method with a dynamical diffusion model based on the Langevin equation. In this approach, the distance of the closest approach for the capture process is estimated within the TDHF approach, which is then plugged into the dynamical diffusion model as an initial condition. We apply this approach to hot fusion reactions leading to formation of the element $Z=120$, that is, the $^{48}$Ca+$^{254,257}$Fm, $^{51}$V+$^{249}$Bk, and $^{54}$Cr+$^{248}$Cm reactions. Our calculations indicate that the distances of the closest approach for these systems are similar to each other and thus the difference in the probabilities of evaporation residue formation among those reaction systems originates mainly from the evaporation process, which is sensitive to the fission barrier height and the excitation energy of a compound nucleus., Comment: 5 pages, 2 figures, 1 table; published in Physical Review C as a Rapid Communication with Editors' Suggestion

Background: In heavy-ion induced reactions, the sub-barrier fusion cross sections are found to be higher as compared to the predictions of the one-dimensional barrier penetration model. Attempts have been made to explain sub-barrier fusion enhancement by including the static deformations, the couplings to inelastic excitations, and non-fusion channels.Purpose: To investigate factors which influence the sub-barrier fusion in the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system and to understand the interplay of couplings, the fusion excitation function was measured at energies from $10%$ below to $15%$ above the Bass barrier.Method: The fusion excitation function was measured by employing a recoil mass spectrometer, the Heavy-Ion Reaction Analyser (HIRA), at the Inter-University Accelerator Centre, New Delhi. To study the behavior of the fusion excitation function and the effect of couplings at sub-barrier energies, the excitation function was analyzed in the framework of the coupled-channels code ccfull.Results: In the present work, the fusion cross section was measured down to 1 $\ensuremath{\mu}\mathrm{b}$ at the lowest measured energy, i.e., $10%$ below the barrier. It was found that the inclusion of couplings of low-lying excited states along with the modified barrier between interacting nuclei satisfactorily reproduces the fusion excitation function of the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system. For better insight into the sub-barrier fusion, the fusion barrier distribution, the logarithmic derivative L(E) factor, and the astrophysical S factor were extracted from the analysis of the experimentally measured fusion excitation function.Conclusions: The analysis of the fusion excitation function in terms of the astrophysical S factor and the L(E) factor suggests the absence of fusion hindrance in the $^{37}\mathrm{Cl}+^{130}\mathrm{Te}$ system down to a 1 $\ensuremath{\mu}\mathrm{b}$ cross section achieved at the lowest measured energy. The excitation function of the present system is compared with the existing measurements in which $^{37}\mathrm{Cl}$ has been used as a projectile to understand the interplay of entrance-channel parameters in sub-barrier fusion enhancement.

Background: Several Time-Dependent Hartree-Fock-Bogoliubov (TDHFB) calculations predict that the super- fluidity enhances the fluctuations of the fusion barrier. This effect is not fully understood and not yet revealed experimentally. Purpose: The goal of this study is to investigate empirically the effect of the superfluidity on the fusion barrier width. Method: First, the local regression method is introduce and used to determine the barrier distribution more precisely. A second method that requires only the calculation of an integral of the cross section is developed to determine accurately the fluctuations of the barrier. A benchmark is done between this two methods and with the fitting method usually used. This integral method showing a better agreement in a test case, it is applied systematically in a selection of 115 fusion reactions. Results: The fluctuations of the barrier for superfluid systems are on average larger than for magic or semi-magic nuclei. This is due to the deformation effects and the effect of the superfluidity. To disentangle those two effects, we compare the experimental width to the width estimated from a model that takes into account the tunneling, the deformation and the vibration effect. The deviation of the experimental width from this theory for reaction between superfluid nuclei shows that the superfluidity enhance the fusion barrier width. Conclusions: This analysis shows that the predicted effect of the superfluidity on the width of the barrier is real and is of the order of 1 MeV., 11 pages, 14 figures

Excitation functions of reaction residues produced in the $^{14}\mathrm{N}+^{169}\mathrm{Tm}$ system have been measured to high precision at energies above the fusion barrier, ranging from $1.04{V}_{B}$ to $1.30{V}_{B}$, and analyzed in the framework of the statistical model code pace4. Analysis of $\ensuremath{\alpha}$-emitting channels points toward the onset of incomplete fusion even at slightly above-barrier energies where complete fusion is supposed to be one of the dominant processes. The onset and strength of incomplete fusion have been deduced and studied in terms of various entrance channel parameters. Present results together with the reanalysis of existing data for various projectile-target combinations conclusively suggest strong influence of projectile structure on the onset of incomplete fusion. Also, a strong dependence on the Coulomb effect $({Z}_{P}{Z}_{T})$ has been observed for the present system along with different projectile-target combinations available in the literature. It is concluded that the fraction of incomplete fusion linearly increases with ${Z}_{P}{Z}_{T}$ and is found to be more for larger ${Z}_{P}{Z}_{T}$ values, indicating significantly important linear systematics.

In this study, the role of bombarding energy in analyzing the interaction potentials and describing the densities of interacting nuclei during fusion is investigated. For this purpose, the fusion cross sections of the $^{40}\mathrm{Ca}+^{48}\mathrm{Ca}, ^{16}\mathrm{O}+^{92}\mathrm{Zr}$, and $^{40}\mathrm{Ca}+^{90}\mathrm{Zr}$ systems are calculated by the use of potentials derived from the semiclassical Skyrme energy density functional and the coupled-channel formalism. The comparisons drawn between the theoretical fusion data and the experimental ones demonstrate the energy-dependence behavior of the potentials employed in the calculations. Considering this dependence, we also show the variations of the density parameters of the colliding nuclei with the bombarding energy. The obtained results indicate that with increasing energy, the fusion barrier heights increase, while the diffuseness parameters of the densities decrease.

The relative yield of complete fusion and quasifission components for the $^{12}\mathrm{C}+^{204}\mathrm{Pb}, ^{19}\mathrm{F}+^{197}\mathrm{Au}, ^{30}\mathrm{Si}+^{186}\mathrm{W}$, and $^{48}\mathrm{Ca}+^{168}\mathrm{Er}$ reactions which all lead to the compound nucleus $^{216}\mathrm{Ra}$ are analyzed to calculate the entrance channel effects by comparison of capture, complete fusion, and quasifission cross sections, emission barriers (${B}_{\mathrm{fus}}^{*},{B}_{qf}$), as well as complete fusion probability estimated by statistical method within the framework of the dinuclear system model. The difference among complete fusion probabilities calculated by the dinuclear system model for different entrance channels can be explained by the hindrance to complete fusion due to the larger inner fusion barrier ${B}_{\mathrm{fus}}^{*}$ for the transformation of the dinuclear system into a compound nucleus and the increase of the quasifission contribution due to the decreasing of the emission barrier ${B}_{qf}$ of quasifission as a function of the angular momentum. Although these reactions with different entrance channels populate the same compound nucleus $^{216}\mathrm{Ra}$ at similar excitation energies, the model predicts the negligible quasifission probability for reactions having higher entrance channel mass asymmetry and the dominant decay channel is complete fission. For reactions induced by massive projectiles such as $\mathrm{Si}$ and $\mathrm{Ca}$ having lower entrance channel mass asymmetry, the quasifission component is dominant in the evolution of dinuclear system, and the fusion process is extremely hindered.

The evaporation residue yields from the compound nuclei $^{220}\mathrm{Th}$ formed in the $^{16}\mathrm{O}+^{204}\mathrm{Pb}, ^{40}\mathrm{Ar}+^{180}\mathrm{Hf}, ^{82}\mathrm{Se}+^{138}\mathrm{Ba}$, and $^{124}\mathrm{Sn}+^{96}\mathrm{Zr}$ reactions are analyzed to study the entrance channel effects by comparison of the capture, fusion, and evaporation residue cross sections calculated by the combined dinuclear system (DNS) and advanced statistical models. The difference between evaporation residue (ER) cross sections can be related to the stages of compound nucleus formation and/or its survival against fission. The sensitivity of both stages in the evolution of the DNS up to the evaporation residue formation to the angular momentum of DNS is studied. The difference between fusion excitation functions is explained by the hindrance to complete fusion due to the larger intrinsic fusion barrier ${B}_{\mathrm{fus}}^{*}$ for the transformation of the DNS into a compound nucleus and the increase of the quasifission contribution due to the decreasing of the quasifission barrier ${B}_{\mathrm{qf}}$ as a function of the angular momentum. The largest value of the ER residue yields in the very mass asymmetric $^{16}\mathrm{O}+^{204}\mathrm{Pb}$ reaction is related to the large fusion probability and to the relatively low threshold of the excitation energy of the compound nucleus. Due to the large threshold of the excitation energy (35 MeV) of the $^{40}\mathrm{Ar}+^{180}\mathrm{Hf}$ reaction, it produces ER yields less than the almost mass symmetric $^{82}\mathrm{Se}+^{138}\mathrm{Ba}$ reaction having the lowest threshold value (12 MeV).

The fission fragment angular distributions were measured at energies above the fusion barrier, for the systems {sup 11}B and {sup 19}F + {sup 238}U. An analysis of the present data along with those already available for the systems {sup 6,7}Li, {sup 12}C, and {sup 16}O + {sup 238}U was made in terms of the saddle-point statistical model. While the anisotropies were ``normal`` for {sup 6,7}Li, {sup 11}B, {sup 12}C+{sup 238}U systems, the ones for {sup 16}O and {sup 19}F+{sup 238}U systems were found to be ``anomalous.`` The entrance channel mass asymmetry dependence of the anisotropies as observed here is consistent with the expectations of preequilibrium fission dynamics. This result emphasizes the importance of preequilibrium fission in heavy-ion induced fusion-fission reactions.

The fission cross sections for [sup 32]S+[sup 138]Ba and [sup 48]Ti+[sup 122]Sn in the regoin of the fusion barrier have been measured. These results are combined with evaporation residue cross sections from another measurement to obtain the total fusion excitation functions for these systems at energies near and below the barrier. Coupled channels calculations easily reproduce the experimental results.

Evaporation residue excitation functions and \ensuremath{\alpha}-multiplicities from complete fusion of $^{16}\mathrm{O}$ with $^{197}\mathrm{Au}$ and $^{208}\mathrm{Pb}$ have been measured from the fusion threshold up to 140 MeV incident energy. The data allow the conclusion that strongly overdamped motion cannot be dominant at energies in the vicinity of the fusion barrier below ${\mathit{E}}^{\mathrm{*}}$\ensuremath{\approxeq}50 MeV. At excitation energies above 50 MeV the residue cross section for $^{16}\mathrm{O}$${+}^{208}$Pb is much greater than predicted from the statistical model with conventional parametrizations. The enhancement is not explained by incorporating dynamical effects into the analysis. An alternative suggestion based on deexcitation-chain dependent fission barriers is discussed.

Using the three versions of proximity potentials, namely proximity 1977, proximity 1988, and proximity 2000, we present a pocket formula for fusion barrier heights and positions. This was achieved by analyzing as many as 400 reactions with mass between 15 and 296. Our parametrized formula can reproduced the exact barrier heights and positions within an accuracy of $\pm1%$. A comparison with the experimental data is also in good agreement., 12 pages, 5 figures

Complete fusion cross sections for {sup 9}Be incident on {sup 208}Pb and {sup 209}Bi have been measured at energies greater than the fusion barrier to investigate the large differences in their reported complete fusion cross sections. Relative xn and fission cross sections are in good agreement. Thus, it is concluded that the differences arise from errors in absolute normalization in the previous measurements. The present measurements show that the above-barrier complete fusion cross sections for the reactions of {sup 9}Be with {sup 209}Bi and {sup 208}Pb are very similar, which resolves the previously observed anomaly. Complete fusion for the reaction of {sup 9}Be with {sup 209}Bi is found to be suppressed by {approx}32% compared to the expectations of a single-barrier penetration model, which is in close agreement with the value previously determined for the reaction with {sup 208}Pb.

We verify that quasi-elastic (elastic$+$inelastic) backscattering barrier distributions for weakly-bound systems do not strictly correspond to fusion barrier distributions, but rather to a reaction threshold distribution, as proposed by Zagrebaev [Phys. Rev. C 78, 047602 (2008)] in a recent paper concerning very heavy systems.

We discuss the use of reduced fusion cross sections in the derivation of fusion barrier distributions. We show that the elimination of static effects associated with system sizes and optical potentials obtained by the recently introduced fusion functions can be extended to barrier distributions. This can be a useful tool for systematic studies of breakup coupling effects in fusion processes.

It is shown that the 'barrier distribution' derived from quasi-elastic backscattering of heavy ions gives us, in fact, information about the 'total reaction threshold distribution' and not about the 'fusion barrier'.

We study fusion reactions of the {sup 64}Ni+{sup 64}Ni system using the density-constrained time-dependent Hartree-Fock (TDHF) formalism. In this formalism the fusion barriers are directly obtained from TDHF dynamics. In addition, we incorporate the entrance channel alignments of the slightly deformed (oblate) {sup 64}Ni nuclei resulting from dynamical Coulomb excitation. We show that alignment leads to a fusion barrier distribution and alters the naive picture for defining which energies are actually sub-barrier. We also show that core orientation effects could play a significant role in fusion cross section calculations.

A modified Woods-Saxon potential model is proposed for a unified description of the entrance channel fusion barrier and the fission barrier of fusion-fission reactions based on the Skyrme energy-density functional approach. The fusion excitation functions of 120 reactions have been systematically studied. The fusion (capture) cross sections are well described with the calculated potential and an empirical barrier distribution. Incorporating a statistical model (HIVAP code) for describing the decay of the compound nucleus, the evaporation residue (and fission) cross sections of 51 fusion-fission reactions have been systematically investigated. Optimal values of some key parameters of the HIVAP code are obtained based on the experimental data of these reactions. The experimental data are reasonably well reproduced by the calculated results. The upper and lower confidence limits of the systematic errors of the calculated results are given., 24 pages, 13 figures, 3 tables, accepted for publication in Phys. Rev. C

A precise fusion excitation function has been measured for 40 Ca+ 94 Zr at near- and sub-barrier energies, and the fusion barrier distribution has been extracted. Comparing with the existing data for 40,48 Ca+ 90,96 Zr shows that couplings to inelastic excitations determine the fusion cross sections and the shape of the barrier distributions near the barrier. At lower energies, the two systems possessing neutron-transfer channels with large positive Q-values ( 40 Ca+ 94,96 Zr) have remarkably similar cross sections, and both show a large enhancement with respect to the other systems and to coupled-channels calculations including up to three quadrupole and octupole phonons in the Zr targets.

The nucleus-nucleus potential for the fusion reactions {sup 40}Ca+{sup 48}Ca, {sup 16}O+{sup 208}Pb, and {sup 48}Ca+{sup 48}Ca has been calculated using the Monte Carlo method. The results obtained indicate that the technique employed for the calculation of the nucleus-nucleus potential is an efficient one. The effects of the spin and the isospin terms have also been studied using the same technique. The analysis of the results obtained for the {sup 48}Ca+{sup 48}Ca reaction reveal that the isospin-dependent term in the nucleon-nucleon potential causes the nuclear potential to drop by an amount of 0.5 MeV. The analytical calculations of the fusion cross section, particularly those at energies less than the fusion barrier, are in good agreement with the experimental data. In these calculations the effective nucleon-nucleon potential chosen is of the M3Y-Paris potential form and no adjustable parameter has been used.

The double-folding model with an M3Y effective nucleon-nucleon (NN) interaction was applied to obtain the angle-dependent bare nucleus-nucleus potential for heavy-ion fusion reactions involving deformed target nuclei. The angular dependence with a zero-range exchange NN interaction is almost identical to that with a finite-range interaction, allowing quick calculations of the fusion cross sections and corresponding barrier distributions $D({E}_{c.m.})$. Since in the literature the experimental $D({E}_{c.m.})$ have been analyzed usually using a Woods-Saxon shape for the nuclear part of the nucleus-nucleus potential, we fitted the spherical double-folding potentials at the barrier radii with a Woods-Saxon (WS) form. The calculated $D({E}_{c.m.})$ with this fitted WS potential, but now accounting for the deformation of the target nuclei, are significantly different from the $D({E}_{c.m.})$ calculated directly using the double-folding potential. This indicates that the finite size effects are substantial and should not be ignored in the analysis of experimental fusion cross sections and barrier distributions for reactions with statically deformed nuclei.

The Langevin equation was used to describe fusion dynamics in two systems, $^{64}\mathrm{Ni}+^{100}\mathrm{Mo}$ and $^{64}\mathrm{Ni}+^{96}\mathrm{Zr}$. The corresponding fusion cross sections were calculated for different energies, and the mean angular momentum and its dependence on energy were also obtained. We were able to reproduce experimental fusion cross sections at high energies with the one-body dissipation mechanism. Attention was focused on the fusion barrier calculated with the Yukawa-plus-exponential method.

The fission fragment mass ratio distributions of fusion-fission events have been measured for the reactions of $^{19}\mathrm{F}+^{232}\mathrm{Th},^{16}\mathrm{O}+^{235}\mathrm{U}$, and $^{16}\mathrm{O}+^{238}\mathrm{U}$ at energies near and below the fusion barrier. It is found that the mass ratio widths follow a decreasing trend with decreasing energy, contrary to recent claims of anomalous mass widths attributed to a quasifission mechanism.

α-Particle singles and doubles yields for the reaction of 9Be+208Pb have been measured from below to well above the fusion barrier energy. These yields have been reproduced by calculations including both neutron transfer and inelastic excitation. The calculations predict breakup cross sections to persist to very low energies, where the latter process dominates.

Fusion cross sections have been measured for the symmetric system ${}^{46}\mathrm{Ti}{+}^{46}\mathrm{Ti}$ in the energy range encompassing the Coulomb barrier. A representation of the fusion barrier distribution has been obtained from the second energy derivative of the excitation function. The data are well described by coupled-channels calculations including two quadrupole phonons and one octupole phonon of both colliding nuclei. The comparison with previous data for ${}^{40}\mathrm{Ca}{+}^{46}\mathrm{Ti}$ and ${}^{40}\mathrm{Ca}{+}^{40}\mathrm{Ca}$ clarifies the relative importance of various low-lying inelastic exitations of ${}^{46}\mathrm{Ti}$ and of ${}^{40}\mathrm{Ca}$ in the subbarrier fusion yields. Similarities with the case of ${}^{58}\mathrm{Ni}{+}^{60}\mathrm{Ni}$ are pointed out.

Precise excitation functions for the fusion of ${}^{12}\mathrm{C},$ ${}^{16}\mathrm{O},$ ${}^{28}\mathrm{Si},$ and ${}^{35}\mathrm{Cl}$ on ${}^{92}\mathrm{Zr}$ were measured for bombarding energies spanning the Coulomb barrier regions. Experimental fusion barrier distributions were derived from these data and compared with the results of realistic coupled-channels calculations, which included couplings to all orders and treated excitation energies correctly. To gain reasonable agreement for the heavier projectiles it was necessary to include double-phonon excitations of the first ${2}^{+}$ and ${3}^{\ensuremath{-}}$ vibrational states in ${}^{92}\mathrm{Zr}.$ The diffuseness parameter required to fit the high-energy cross sections increases with increasing charge of the projectile and, as found in earlier work, is higher than that required to fit elastic-scattering data. It is suggested that a potential which falls more rapidly at large distance than the Woods-Saxon form might help explain the anomaly.

We calculate the formation cross sections of transactinides (superheavy elements), as well as heavy actinides (No and Lr), which have been or might be obtained in fusion reactions with the evaporation of only one neutron. We use both more realistic fusion barrier and survival probability of the compound nucleus in comparison with the original phenomenological model [Phys. Rev. C 59, 2634 (1999)] that prompted the Berkeley experiment on the synthesis of a new superheavy element 118 [Phys. Rev. Lett. 83, 1104 (1999)]. Calculations are performed for asymmetric and symmetric target-projectile combinations and for reactions with stable and radioactive-ion beams. The formation cross sections measured at GSI-Darmstadt for transactinides and heavy actinides, as well as that for superheavy element 118 reported by the LBNL-Berkeley group, are reproduced within a factor of 2.4, on average. Based on the obtained relatively large cross sections, we predict that optimal reactions with stable beams for the synthesis of so far unobserved superheavy elements 119, 120, and 121 are ${}^{209}\mathrm{Bi}{(}^{86}\mathrm{Kr}, {1n)}^{294}119,{ }^{208}\mathrm{Pb}{(}^{88}\mathrm{Sr}, {1n)}^{295}120,$ and ${}^{209}\mathrm{Bi}{(}^{88}\mathrm{Sr}, {1n)}^{296}121,$ respectively. This is because of the magic of both the target and the projectile that leads to larger Q value and, consequently, lower effective fusion barrier with larger transmission probability. The same effect is responsible for relatively large cross sections predicted for the symmetric reactions ${}^{136}\mathrm{Xe}{(}^{124}\mathrm{Sn}, {1n)}^{259}\mathrm{Rf},{ }^{136}\mathrm{Xe}{(}^{136}\mathrm{Xe}, {1n)}^{271}\mathrm{Hs}{,}^{138}\mathrm{Ba}{(}^{136}\mathrm{Xe}, {1n)}^{273}110,$ and ${}^{140}\mathrm{Ce}{(}^{136}\mathrm{Xe}, {1n)}^{275}112.$ Although shell effects in the magic nuclei ${}^{124}\mathrm{Sn},{ }^{136}\mathrm{Xe},{ }^{138}\mathrm{Ba},$ and ${}^{140}\mathrm{Ce}$ are not as strong as in ${}^{208}\mathrm{Pb}$ and ${}^{209}\mathrm{Bi},$ they act on both the target and the projectile and lead to the prediction of measurable cross sections.

Fusion cross sections were measured for the systems 16O and 28Si+ 120Sn in order to understand the role of specific channels involved in sub-barrier fusion. Fusion cross sections were measured by direct detection of the evaporation residues. Extracted fusion barrier distributions were analyzed using the exact coupled-channel code CCFULL as well as the simplified code CCMOD. These calculations show that the observed fusion barrier distribution for the Si+Sn system is reproduced only if the rotational excitation in 28Si is taken into account.

Analyses using simplified coupled-channels models have been unable to describe the shape of the previously measured fusion barrier distribution for the doubly magic ${}^{16}\mathrm{O}{+}^{208}\mathrm{Pb}$ system. This problem was investigated by remeasuring the fission excitation function for ${}^{16}\mathrm{O}{+}^{208}\mathrm{Pb}$ with improved accuracy and performing more exact coupled-channels calculations, avoiding the constant-coupling and first-order coupling approximations often used in simplified analyses. Couplings to the single- and 2-phonon states of ${}^{208}\mathrm{Pb},$ correctly taking into account the excitation energy and the phonon character of these states, particle transfers, and the effects of varying the diffuseness of the nuclear potential, were all explored. However, in contrast to other recent analyses of precise fusion data, no satisfactory simultaneous description of the shape of the experimental barrier distribution and the fusion cross sections for ${}^{16}\mathrm{O}{+}^{208}\mathrm{Pb}$ was obtained.

The effects of long range absorption on the distribution of fusion barriers are discussed under eigenchannel approximations. It is shown that due to channel coupling effects, the upper fusion barrier cannot be extracted unambiguously using any coupled channel codes based on optical model approaches.

The internuclear potential determined from published fusion barrier parameters is compared with the proximity potential of Blocki et al. Discussion is given of the uncertainties introduced into the data analysis by the effects of friction and errors in the barrier radii.

Absolute yields, energy spectra, and angular distributions of heavy residual nuclei ranging from Ne to Si have been measured in the reactions $^{16}\mathrm{O}$ + $^{12}\mathrm{C}$, $^{17}\mathrm{O}$ + $^{12}\mathrm{C}$, and $^{18}\mathrm{O}$ + $^{12}\mathrm{C}$. For each system measurements have been performed at seven beam energies corresponding to the range 7 to 14 MeV c.m. The formation of the above products is shown to be consistent with a reaction which proceeds through the formation and decay of an excited and equilibrated composite system. Systematic differences between the absolute magnitudes of the fusion cross sections of the three reactions have been observed. It is shown that these differences are closely related to the expected differences in the nuclear size and surface diffuseness of the oxygen isotopes. Possible implications for astrophysical processes are briefly discussed.NUCLEAR REACTIONS Complete fusion of $^{16}\mathrm{O}$ + $^{12}\mathrm{C}$, $^{17}\mathrm{O}$ + $^{12}\mathrm{C}$, and $^{18}\mathrm{O}$ + $^{12}\mathrm{C}$ at $E=7\ensuremath{-}14$ MeV c.m. Measured $\ensuremath{\sigma}(E,\ensuremath{\theta})$ of evaporation residues. Deduced fusion barrier characteristics.

Using ..gamma..-ray photopeak intensities, excitation functions of one-neutron transfer to excited states in reaction products have been measured from about 20% and 15% below the fusion barrier to above barrier energies for /sup 58/Ni+ /sup 64/Ni and /sup 64/Ni+ /sup 64/Ni reactions, respectively. For /sup 58/Ni+ /sup 64/Ni, the one-neutron transfer cross section is greater than 1 mb at 20% below the barrier. The results are well described by distorted-wave Born approximation calculations using spectroscopic factors deduced from light-ion transfer measurements.

Measurements of the total fusion cross sections for $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$, $^{13}\mathrm{C}$, $^{14}\mathrm{N}$, $^{15}\mathrm{N}$, $^{16}\mathrm{O}$, $^{18}\mathrm{O}$, and $^{19}\mathrm{F}$ and $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$ have been performed over the energy range from 1.5 to 3 times the Coulomb barrier energy. Fusion barrier parameters were extracted for each system. Three systems, $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$, $^{12}\mathrm{C}$ + $^{16}\mathrm{O}$, and $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$, show rather pronounced oscillatory structure in the energy dependence of the fusion cross sections. The maximum fusion cross sections for the systems studied vary by as much as 10-20%, depending on the particular entrance channel. The specific structure of the interacting nuclei clearly does have an effect; the fusion process is not entirely dominated by the macroscopic features of the ion-ion interaction.NUCLEAR REACTIONS, fusion, measured ${\ensuremath{\sigma}}_{\mathrm{fusion}}(E)$; $^{12}\mathrm{C}$ + $^{12}\mathrm{C}$, $7.4l~{E}_{\mathrm{c}.\mathrm{m}.}l~31.2$ MeV; $^{12}\mathrm{C}$ + $^{13}\mathrm{C}$, $7.6l~{E}_{\mathrm{c}.\mathrm{m}.}l~24.9$ MeV; $^{12}\mathrm{C}$ + $^{14}\mathrm{N}$, $15.1l~{E}_{\mathrm{c}.\mathrm{m}.}l~24.0$ MeV; $^{12}\mathrm{C}$ + $^{15}\mathrm{N}$, $8.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~26.7$ MeV; $^{12}\mathrm{C}$ + $^{16}\mathrm{O}$, $12.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~27.0$ MeV; $^{12}\mathrm{C}$ + $^{18}\mathrm{O}$, $11.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~28.0$ MeV; $^{12}\mathrm{C}$ + $^{19}\mathrm{F}$, $11.6l~{E}_{\mathrm{c}.\mathrm{m}.}l~27.1$ MeV; $^{16}\mathrm{O}$ + $^{16}\mathrm{O}$, $14.9l~{E}_{\mathrm{c}.\mathrm{m}.}l~36.0$ MeV; deduced fusion barrier parameters.

The analysis of quasielastic cross section data for the /sup 90/Zr projectile plus /sup 50/Ti target system shows that the probability for /sup 50/Ti(/sup 90/Zr, /sup 49/Ti)/sup 91/Zr, 1n-transfer reaction near the barrier is much larger than estimates based on semiclassical theory. The probability for /sup 50/Ti(/sup 90/Zr,/sup 51/V)/sup 89/Y, 1p-transfer reaction, on the other hand, agrees with the same theory. The internuclear distance where the 1n-transfer probability first deviates from tunneling predictions coincides with the threshold of the fusion barrier distribution deduced from the experimental fusion cross sections of the /sup 50/Ti+/sup 90/Zr system, suggesting a common mechanism for the large enhancement of 1n-transfer and fusion cross sections.

Fusion cross sections for $^{16}$O${+\mathrm{}}^{16}$O and $^{40}$Ca${+\mathrm{}}^{40}$Ca reactions are calculated in the classical microscopic equations of motion approach. Calculated fusion cross sections are sensitive to the long-range nature of the effective nucleon-nucleon (NN) potential. It is shown that with a proper choice of the parameters of the NN potential, the model calculations give good agreement with experiments over a wide range of energies above the fusion barrier.

Experimental evaporation residue excitation functions are presented for /sup 58/Ni projectiles on /sup 62/Ni targets. These data are analyzed for fusion radii and for the nucleus-nucleus potential at the fusion barrier. The results are compared with predictions of three potential models.

Analytical expressions for the fusion barrier height and radius have been derived from a four-parameter empirical fusion cross section formula for heavy ions. The fusion barrier parameters calculated, using these expressions, are in good agreement with the literature values.

Fusion cross sections have been measured for the system $^{28}\mathrm{Si}$+$^{12}\mathrm{C}$ from 50 to 105 MeV. No markedly smaller fusion cross sections were observed in comparison with the previously reported results for the other isotope systems $^{12}\mathrm{C}$+$^{29,30}\mathrm{Si}$. Furthermore, the average energy dependence of the fusion cross sections for the three systems are well reproduced by the fusion barrier model with the same parameters. The maximum fusion cross sections for these systems are also well interpreted in terms of the statistical yrast line model.

Difficulties associated with the determination of the nuclear potential at distances inside the fusion barrier radius are discussed. The critical distance model analysis of fusion excitation functions at high bombarding energies does not give a model independent measurement of the internuclear potential at small separations of interacting heavy nuclei.